MGF
Units & Measurements abbreviation · Statistics
| Stands for | Moment-generating function |
|---|---|
| Categories | Units & Measurements |
MGF stands for Moment-generating function, a statistics abbreviation.
The function M(t) = E[e^(tX)], whose derivatives at zero give a distribution's moments: the first is the mean, and the second leads to the variance. Distributions with the same MGF are identical.
Example: Using the MGF of the Poisson distribution shows that its mean and variance both equal λ.
Usage notes
MGFs simplify sums of independent variables, because the MGF of a sum is the product of the individual MGFs, which gives a short proof of the central limit theorem. Some distributions, such as the lognormal, have all moments but no MGF; the characteristic function always exists.
Related abbreviations
More statistics abbreviations
- MAP – Maximum a posteriori
- MAPE – Mean absolute percentage error
- MAR – Missing at random
- MCAR – Missing completely at random
- MCMC – Markov chain Monte Carlo
- Mdn – Median
- MLE – Maximum likelihood estimation
- MOE – Margin of error
- MSE – Mean squared error
- n – Sample size
- NPV – Negative predictive value
- OLS – Ordinary least squares